(J. Scott Applewhite/AP)

A new break in the GOP's debt-ceiling strategy emerged at a private lunch on Wednesday, where House Speaker John A. Boehner (R-Ohio) encouraged his allies to consider linking a restoration of recently cut military benefits with a one-year extension of the federal government's borrowing authority.

According to two people present at the lunch and two others familiar with the session, Boehner said the maneuver would likely force Democrats to join with Republicans and also win support from conservatives, who have been upset about changes to the military's cost-of-living benefits, which were adjusted in December.

Boehner did not endorse the idea, the sources added, but he did urge the group of more than a dozen of his loyalists to talk up the possible play with colleagues. And if the idea gains momentum, he is open to potentially bringing it to the floor, they said.

"He was very warm to it, seeing it as something that can get us out of this fix," said one attendee, who like the others requested anonymity to discuss internal deliberations. "I think this could be a way for us to get through the debt ceiling, but the speaker is going to spend the next few days taking the temperature of his members."

The lunch, held at the Capitol, was Boehner's first huddle with his inner circle  since he met with House Republican leaders Wednesday morning. He was informed then that the GOP's leading options for the debt-limit discussions - linking an extension to approval of the Keystone XL pipeline or repealing parts of the Affordable Care Act - had mixed support.

Earlier this week, Senate Majority Leader Harry Reid (D-Nev.) signaled he would like to see a restoration of the previous level of cost-of-living benefits for military personnel, and aides said he is planning to push legislation as early as next week that would return billions of related funding cut under last year’s budget agreement.